Description
- Abstract:
- We consider a discrete attachment model for the self-assembly of polyhedra called the Building Game. The combinatorial configuration space of the model is computed for the Polyhedra in the Platonic, Archimedean, and Catalan solids of up to 30 faces and several novel enumerative results are generated. Further, we extend the Building Game to include geometric information in the form of a polygonal linkage. Using systems of constraints to specify the linkage, the geometric configuration space is given as a solution manifold. A random walk scheme is used to simulate reflected Brownian motion on the geometric configuration space manifolds. The combinatorial and geometric aspects of the Building Game are combined and used in a Markov process model for measuring statistics of the self-assembly process.
- Notes:
- Thesis (Ph.D. -- Brown University (2015)
Access Conditions
- Rights
- In Copyright
- Restrictions on Use
- Collection is open for research.
Citation
Johnson, Daniel C.,
"Combinatorial and Geometric Structure in the Self-Assembly of Polyhedra"
(2015).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0ZK5F37
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....